integral of x\sqrt[3]{x+17}

Lösung

\int x 3 x + 17 d x

\frac{3}{7} (x + 17)^{\frac{7}{3}} - \frac{51}{4} (x + 17)^{\frac{4}{3}} + C

Schritte zur Lösung

\int x 3 x + 17 d x

Wende U-Substitution an

= \int (u - 17) 3 u d u

Multipliziere aus

(u - 17) 3 u : u^{\frac{4}{3}} - 17 3 u

= \int u^{\frac{4}{3}} - 17 3 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{4}{3}} d u - \int 17 3 u d u

\int u^{\frac{4}{3}} d u = \frac{3}{7} u^{\frac{7}{3}}

\int 17 3 u d u = \frac{51}{4} u^{\frac{4}{3}}

= \frac{3}{7} u^{\frac{7}{3}} - \frac{51}{4} u^{\frac{4}{3}}

Setze in

u = x + 17

ein

= \frac{3}{7} (x + 17)^{\frac{7}{3}} - \frac{51}{4} (x + 17)^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{7} (x + 17)^{\frac{7}{3}} - \frac{51}{4} (x + 17)^{\frac{4}{3}} + C

t an g e n t x + \frac{3}{x}

a re a y = 3 x, x = 1

y^{^{'}} - 3 y = e^{2 x}

\int (x - 6) d x

x \to 0 lim (\frac{e ^{x} - ( 1 - x )}{x})